Accelerated magnetic resonance imaging (“MRI”) acquisition techniques such as partial Fourier, non-Cartesian, parallel imaging, and time-frequency acquisitions have been widely studied over the past few decades. Partial Fourier methods use phase information to reduce scan time. Non-Cartesian sampling techniques rely on more efficient k-space transversals and have incoherent or less visually significant artifacts compared to Cartesian sampling. The local sensitivity of phased-array coil elements are used in parallel imaging either in k-space, such as with SMASH and GRAPPA, or image space, such as with SENSE, to allow accelerated data acquisition. In dynamic MRI, such as perfusion or cine imaging, time-frequency approaches such as k-t SENSE, UNFOLD, and TSENSE have been used to accelerate data acquisition by exploiting spatiotemporal information. Despite all these efforts, long scan time is still a main challenge for MRI, especially in cardiac imaging where alternative modalities such as multi-detector CT benefit from rapid acquisition and high patient throughput.
Compressed, or compressive, sensing (“CS”) is a recently developed image reconstruction technique that is applicable for randomly sampled k-space data. This technique exploits the sparsity, or more generally compressibility, of the target image in a transform domain to provide for accelerated data acquisitions. Moreover, CS techniques may be used to surpass the current rapid acquisition techniques in terms of acceleration rate. CS techniques have already been applied in several cardiac applications to reduce scan time, which can be traded off for higher spatial or temporal resolution. CS has also been used in pediatric imaging, non-contrast-enhanced peripheral angiography, three-dimensional upper airway imaging, and hyperpolarized carbon-13 MR spectroscopy. Furthermore, attempts have been made to combine parallel imaging and CS, via sparsity-regularized iterative GRAPPA-type approaches, a concurrent combination of CS and SENSE where the coil sensitivities are used to enforce data consistency in addition to sparsity constraints, and a serial combination of CS and SENSE.
CS reconstruction techniques generally aim to minimize the sparsity of a target image in a transform domain subject to data consistency constraints that compare an image estimate to the acquired k-space data. Minimization of the number of non-zero coefficients, which is a direct measure of sparsity, is NP-hard in general. Thus, alternative measures, such as the l1-norm of the transform domain coefficients have been proposed instead.
Minimization of the convex l1-norm of transform domain coefficients has also been the preferred CS sparsity regularization in MRI for all the aforementioned applications. This technique assumes that an image has a sufficiently sparse representation in a pre-selected transform domain. Although sparsity is a necessary condition for l1-norm reconstruction, it is extremely difficult to know whether a transform can efficiently represent the underlying target image characteristics. For instance, wavelets cannot capture smooth transitions sparsely, whereas finite differences have problems with sharp edges. Thus, minimization of sparsity with a fixed transform domain may result in blurring and other image artifacts. Even if the transform dictionary is generated using the computationally expensive dictionary learning algorithms, the effectiveness of such transforms may degrade due to inter and intra-patient variability, especially for cardiac MRI where contrast and signal levels vary significantly between different acquisitions. Furthermore, such techniques fail to provide a reconstruction strategy that can be applied to various different anatomical features without the need for training data or prior assumption about underlying features. Moreover, since no local information is used, these methods are generally not robust to estimation errors in coil sensitivity maps.
It would therefore be desirable to provide a method for magnetic resonance image reconstruction that includes the scan time reduction benefits of CS techniques, but that is robust to inter- and intra-patient variabilities without the need for separately acquired training data.